Answer Blanks in Limits of Integration

Answer blanks in the limits of integration

Complete Code

POD for Macro Files

PG problem file

Explanation

DOCUMENT();

loadMacros(
    'PGstandard.pl', 'PGML.pl', 'niceTables.pl', 'answerHints.pl',
    'PGcourse.pl'
);

Preamble

We use niceTables.pl for table formatting commands we will use to put the answer blanks in the limits of integration. We use answerHints.pl to help guide students toward the correct answer.

Context()->variables->are(
    x  => 'Real',
    dx => 'Real',
    t  => 'Real',
    dt => 'Real'
);

$integral = LayoutTable(
    [
        [ ' ', ans_rule(4) ],
        [
            '\(f(x)= \)' . ans_rule(10) . '\(+\)',
            '\(\displaystyle \int \;\;\)' . ans_rule(10)
        ],
        [ ' ', ans_rule(4) ],
    ],
    align      => 'rl',
    allcellcss => { padding => '3pt' }
);

Setup

We define both x and t as variables as well as the differential dx (which would be incorrect) and the correct dt.

The LayoutTable of niceTables.pl is used to display the definite integral. Note that the align => 'rl' is used to get the formatting to look correct.

BEGIN_PGML
Find a formula for the function [`f(x)`] such that [`f '(x) = [$fpx]`] and
[`f(2) = 5`].  Use [`t`] as the variable of integration inside the integral.

[$integral]*
END_PGML

Statement

The integral is placed in the problem with the [$integral]* which displays the table.

$fpx = Formula("sin(x)");
$fpt = Formula("sin(t)");

ANS(Compute('x')->cmp());
ANS(Compute('5')->cmp());
ANS(
    Compute("$fpt * dt")->cmp()->withPostFilter(AnswerHints(
        Formula("$fpx")    => "Are you using the correct variable?",
        Formula("$fpx*dx") => "Are you using the correct variable?",
        Formula("$fpt")    => "Don't forget the differential dt",
    ))
);
ANS(Compute('2')->cmp());

Answer

The answer blanks are written out as ans_rule, so we must use this style of answer checking. We use AnswerHints to guide the students to the correct answer. Note that we also include the incorrect answer with the x as the variable and give the student feedback on this.

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.